The access code for a garage door consists of three digits. Each digit can be any number from 1 through 5, and each digit can be repeated. Complete parts (a) through (c). (a) Find the number of possible access codes. (b) What is the probability of randomly selecting the correct access code on the first try? (c) What is the probability of not selecting the correct access code on the first try? (a) Find the number of possible access codes. The number of different codes available is nothing.

(a) 125

Step-by-step explanation:

We are given that access code consists of 3 digits.

Each digit can be any digit through 1 to 5 and can be repeated.

Now, this problem is equivalent to the problem that we have to find:

The number of 3 digit numbers that can be formed using the digits 1 to 5 with repetition allowed.

(a) We have 3 places here, unit's, ten's and hundred's places respectively and  each of the 3 places have 5 possibilities (any digit allowed with repetition).

So, total number of access codes possible:

(b) Suppose, an access code is randomly selected, what is the probability that it will be correct.

Formula for probability of an event E can be observed as:

Here, only 1 code is correct, so

Number of favorable cases = 1

Total number of cases = 125

So, required probability:

(c) Probability of not selecting the correct access code on first time:

So, the answers are:

(a) 125

560

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